Lax equivalence theorem

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In numerical analysis, the Lax equivalence theorem states a consistent finite difference approximation for a well-posed linear initial value problem is convergent if and only if it is stable. [1]

This theorem is due to Peter Lax. It is sometimes called the Lax–Richtmyer theorem, after Peter Lax and Robert D. Richtmyer.[2][3][4]

[edit] References

  1. ^ Strikwerda, John C. (1989), Finite Difference Schemes and Partial Differential Equations (1st ed.), Chapman & Hall, pp. 26, 222 
  2. ^ John Gary, A Generalization of the Lax-Richtmyer Theorem on Finite Difference Schemes SIAM Journal on Numerical Analysis, Vol. 3, No. 3 (Sep., 1966), pp. 467--473 JSTOR
  3. ^ Richtmyer, Robert D.; Morton, K. W. Difference methods for initial-value problems. Reprint of the second edition. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1994. xiv+405 pp. ISBN 0-89464-763-6 MR1275838
  4. ^ Lax, P. D.; Richtmyer, R. D. Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9 (1956), 267--293 MR0079204 doi:10.1002/cpa.3160090206

[edit] External links


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